What is Interpretation: Definition and 831 Discussions

An interpretation is an assignment of meaning to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning until they are given some interpretation. The general study of interpretations of formal languages is called formal semantics.
The most commonly studied formal logics are propositional logic, predicate logic and their modal analogs, and for these there are standard ways of presenting an interpretation. In these contexts an interpretation is a function that provides the extension of symbols and strings of symbols of an object language. For example, an interpretation function could take the predicate T (for "tall") and assign it the extension {a} (for "Abraham Lincoln"). Note that all our interpretation does is assign the extension {a} to the non-logical constant T, and does not make a claim about whether T is to stand for tall and 'a' for Abraham Lincoln. Nor does logical interpretation have anything to say about logical connectives like 'and', 'or' and 'not'. Though we may take these symbols to stand for certain things or concepts, this is not determined by the interpretation function.
An interpretation often (but not always) provides a way to determine the truth values of sentences in a language. If a given interpretation assigns the value True to a sentence or theory, the interpretation is called a model of that sentence or theory.

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  1. ilasus

    I Another interpretation of Lorentz transformations

    I consider three material points O, O', M, in uniform rectilinear motion in a common direction, so that in relation to the point O, the points O' and M move in the same direction with the constant velocities v and u (u>v>0). Assuming that at the initial moment (t0=0), the points O, O', M were in...
  2. Adrian59

    A Is the CMBR interpretation for dark matter a fudge?

    The likelihood for dark matter appears to be lessening in direct detection and in its utility in explaining astronomical anomalies. With regard to the former, a trio of recent dark matter detection experiments (LUX 2016, PandaX II 2017 and Xenon1t 2018) have all failed to show any non-baryonic...
  3. T

    I Are there signs that any Quantum Interpretation can be proved or disproved?

    The concept of decoherence seems to be a major progress in quantum mechanics. Has decoherence or any other new finding the potential that a particular interpretation of quantum mechanics will prove correct or incorrect resp. in the foreseeable future?
  4. AdvaitDhingra

    QFT interpretation of Hawking Radiation

    Hello, So I was reading about Hawking radiation and I read a QFT interpretation of it. It went something like this: A vacuum contains virtual particles (vacuum energy), which in qft can be described as waves that are out of phase and cancel each other out (matter and antimatter). I a black...
  5. JD_PM

    A How to construct a diagrammatic interpretation out of ##Z[J]##

    I am aimed at understanding how to derive the Feynman rules out of a generating functional ##Z[J]##, which depends on the set of coordinates ##x=(x_1,...,x_n)^T \in \Bbb R^n## and Grassmann variables ##\bar{\theta}, \theta## \begin{equation} Z[J] := \frac{1}{(2 \pi)^{n/2}} \int d^n x...
  6. mitochan

    I Question on number of generated worlds in many world interpretation

    Hello. I am curious to learn many world interpretation. In collapse of state 3/5 |0>+ 4/5 |1> to |0> or |1>, it jumps to |0> with probability 9/25 or to |1> with probability 16/25. In many world interpretation I assume 9 worlds of |0> and 16 worlds of |1> so total 25 (or its multiple)...
  7. OlegKmechak

    Is there some geometrical interpretation of force from Newton's Laws?

    dP = F dt dE = F dr or if we introduce ds = (dt, dr) (dP, dE) = F ds And both dP and dE are constant in closed system. Some questions: - How does its implies on definition of Force? - Is there some clever geometrical interpretation of Force? - Why P and E seems almost interchengable?
  8. Demystifier

    A Criteria for a good quantum interpretation

    Matt Leifer gives criteria that any good quantum interpretation should satisfy. http://mattleifer.info/2006/06/28/professional-jealousy/?fbclid=IwAR2wl5kEzcfbn6doA53UMty42JP5dADhA5SDxRjaTMNPkq1i9Ag3WPCwB5Q
  9. Demystifier

    A The minimal statistical interpretation is neither minimal nor statistical

    Those days I'm in the mood of criticizing the Ballentine's statistical interpretation, also known as the minimal statistical interpretation. Here I will argue that it is, in fact, neither minimal nor statistical. The main culprit is that Ballentine repeatedly insists that there is no wave...
  10. J

    I The Ensemble Interpretation and the Double Slit Experiment

    I am a big fan of Ballentine's book on QM and was reading the discussions about the Ensemble Interpretation. Although, I am not an expert on these matters I reject the idea of the wave function collapse as a fundamental postulate of QM. Instead, I've come to the conclusion that we don't...
  11. Demystifier

    A Is the Ensemble Interpretation Inconsistent with the PBR Theorem?

    [Moderator's note: Spun off from another thread due to topic and subforum change.] I think Ballentine's interpretation is ruled out by the PBR theorem. Maybe we could discuss that?
  12. zonde

    I Interpretation of Potential Energy as Field Property

    I will quote this statement from another thread: In that thread number of other posters seemed to agree with this statement. So I tried to analyze it a bit. For the sake of my questions let's say we limit GR to Schwarzschild spacetime and if there are problems with gravitational potential...
  13. EclogiteFacies

    I Consistent Histories Interpretation - History

    I have just finished reading the book 'Three Roads to Quantum Gravity' by Lee Smolin. My question interestingly is associated with my geology background. Lee Smolin notes Fay Dowker concludes that if Consistent Histories is true then we cannot deduce the existence of dinosaurs 100 million...
  14. S

    A Question on many world interpretation of Quantum Theory

    Every second the universe branches into 5000 universes and each of those 5000 universes branches into 5000 more after one more second. Now, consider an 80 year old person, he has lived close to 80*365*24*60*60 seconds, which is 2.5 Billion seconds. So, in his life time, universe has branched...
  15. Duplex

    MWI interpretation and free-will compatible?

    I am in my self-driving car and approaching an intersection, where I can either drive to the right or left. I choose to drive to the right. There are two buttons on the instrument panel, R (ight) and L (eft). I press R, and a QM random number generator is activated. My car drives to the right...
  16. D

    I What is the Copenhagen interpretation according to its originator(s)?

    I feel that contemporary authors' statements about the copenhagen interpretation don't really match with what the founders of quantum mechanics said. Also, different authors give seemingly contradictory statements about it is. What do the members here think about this? What is the copenhagen...
  17. entropy1

    I Probability in MWI and the Copenhagen interpretation

    Suppose we have an operator with three eigenvectors/eigenvalues ##e_1##, ##e_2## and ##e_3##. The operator measures wavefunction ##\psi##. Could we say that we find outcome ##e_x## with probability ##P(\psi,e_x)##, and could we extend this to an infinite dimensional operator as a spectrum of...
  18. B

    I Interpretation of quantum theories through the interpretation of classical ones

    Perhaps the reason is that the principle of least action is elevated to a divine principle that does not require materialistic interpretation. If so, then the solution to the "secrets" of quantum theories lies in the solution of the materialistic essence of the physical magnitude of action.
  19. BohmianRealist

    I A non-branching interpretation of the universal wavefunction

    Would it make sense to say that the entire evolutionary history of the universal wavefunction could simply be a single, continuous moment of self-measurement? In other words, that the universe exists for no other reason than to be the apparatus that is always in the process of measuring its own...
  20. thaiqi

    Quantum Nelson's Stochastic Interpretation of QM: Which Material is Best?

    Hello,everyone. Which material is best for Nelson's stochastic interpretation of quantum mechanics?
  21. F

    I What is an interpretation of wave of field?

    What is an interpretation of wave of field(wave that its medium is field) in QFT?Is it correct that the trajectory that wave propagates is the "classical trajectory" of particle created by the field?
  22. Q

    I What is the current perspective on quantum interpretation?

    Back in the day, there were a few Quantum Interpretation polls on here, as of late I have not seen any. I love that we now have a sub-forum for Foundations discussions. I figured it would be interesting to see how the participants of PhysicsForums feel about the different interpretations these...
  23. G

    I Is there a name for this type of interpretation?

    One hypothesis (may be a mainstream interpretation now, I didn't follow this subject very closely) about why "quantum communication" isn't possible using quantum entanglement is that we as observers, the physicists who conduct such experiments are automatons, and that at which instant would he...
  24. johnconner

    I Copenhagen interpretation & Delayed-choice quantum eraser

    For explaining Delayed-choice quantum eraser experiment, what if I change the Copenhagen interpretation a little. When the experiment is concluded, we observe one detector (the first detector with the shortest path) has detected the pattern long before the wavefunction is collapsed (before the...
  25. T

    I Role of the collapse in the instrumentalist interpretation

    As I understand it, from the instrumentalist perspective the wavefunction is not more than a mathematical tool which predicts probabilities. So he could say a mathematical tool can't collapse because it is not a real physical thing. So to talk about a collapse of the wavefunction is meaningless...
  26. Lunct

    How can the many worlds interpretation be deterministic?

    So the many worlds interpretation describes every quantum events as a branch point, where in which all events happen. I'll use the example of a coin toss to illustrate my question. If I flip a coin, I create a branch point in my universe from which two universes emerge, where both heads and...
  27. LCSphysicist

    I What are current Physicists' general positions on the Copenhagen Interpretation?

    Actually, is not a doubt as a question, in which there is wrong or right. I just want to update myself with respect to the current physicists opinion about the Copenhagen interpretation of Bohr and Heisenberg. Summarizing, there is a consensus among the majority? In another words, there is still...
  28. What's the Real Meaning of Quantum Mechanics? - with Jim Baggott

    What's the Real Meaning of Quantum Mechanics? - with Jim Baggott

    Jim explores what are the most popular interpretations of quantum mechanics and how we might need to be a little more specific when we talk about ‘reality’. Excellent layman's explanation of the Bell Inequality experiments.
    • Quotidian
    • Media item
    • interpretation philosophy quantum physics
    • Comments: 0
    • Category: Quantum
  29. A. Neumaier

    A Many Worlds versus Thermal interpretation

    The two volume treatise Bryce DeWitt, The global approach to quantum field theory, Oxford Univ. Press 2003. which discusses the canonical approach to dynamical quantum gravity, is probably responsible for the fact that the many worlds interpretation (MWI) of quantum mechanics has a sizable...
  30. Demystifier

    A Is unitarity necessary for the probabilistic interpretation?

    It is usually said that unitarity is necessary for the consistent probabilistic interpretation. But is that really so? Suppose that ##|\psi(t)\rangle## does not evolve unitarily with time, so that ##\langle\psi(t)|\psi(t)\rangle## changes with time. Even then one can propose that probability...
  31. A. Neumaier

    I Steven Weinberg on the interpretation of quantum mechanics

    I think Weinberg is quite clear about this: On p.87 of the second edition of his quantum mechanics book, he says, and on p.88: After having discussed decoherence, he says on p.92: For the instrumentalist approach (apparently your view of the matter), he states on p.92f this drawback: Then...
  32. Lynch101

    I For and Against the Copenhagen Interpretation

    Given the various different interpretations of quantum mechanics, I am interested in getting a general overview of most/all of them. I think it would be interesting to hear what people list as the positives of each interpretation as well as issues they perceive with each. I was thinking that, if...
  33. E

    A Question about the perception of collapse in relational to QM interpretation

    I'm diving into the RQM and one thing still puzzles me. I have hard time understanding this: Taking the model system discussed above, if O′ has full information on the S+O system, it will know the Hamiltonians of both S and O, including the interaction Hamiltonian. Thus, the system will evolve...
  34. binbagsss

    Help with Interpretation of this Quote by Charles Sanders Peirce

    Understand me well. My appeal is to observation- observation that each of you must make for himself" . Charles Sanders Peirce What is your interpretation of this?
  35. jk22

    I Interpretation of "pseudo-diagonalisation"

    I wanted to know what the usage of the following could be : Let ##A\in M_{n\times n}(K)## a matrix over the field K. Suppose we look for ##x,\lambda\in M_{n\times 1}(K)## such that $$Ax=(\lambda_i x_i)$$ Hence instead of having a global eigenvalue we would have local ones. I know the...
  36. Killtech

    I Hydrodynamic interpretation and consistency classic probability

    So back in the other thread I asked about compatibility of classical probability theory (PT) and QM – and it turns out there is no inherent reason why they need to be incompatible. Therefore I was looking for something that makes them compatible, which wasn’t easy to search for. But there seems...
  37. M

    I Schrodinger’s cat and the Many Worlds interpretation

    Schrodinger’s Cat and the many worlds interpretation states that the wave function collapse doesn’t happen at all; every possible outcome of an observation actually comes to pass in its own separate universe. We are presented with a binary (discrete) outcome (dead or alive) but what if there...
  38. M

    MHB Which is the geometric interpretation?

    Hey! :o Which is the geometric interpretation of the following maps? $$v\mapsto \begin{pmatrix} 0&-1&0\\ 1&0&0\\ 0&0&-1\end{pmatrix}v$$ and $$v\mapsto \begin{pmatrix} 1& 0&0\\0&\frac{1}{2} &-\frac{\sqrt{3}}{2}\\ 0&\frac{\sqrt{3}}{2}&\frac{1}{2}\end{pmatrix}v$$
  39. M

    MHB Understanding Map Interpretation and Shadow Projection on a Plane

    Hey! :o Let $\phi_1:\mathbb{R}^3\rightarrow \mathbb{R}^3$, $v\mapsto \begin{pmatrix}0 & -1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1\end{pmatrix}\cdot v$, $\phi_2:\mathbb{R}^3\rightarrow \mathbb{R}^3$, $v\mapsto \frac{1}{3}\begin{pmatrix}2 & - 1& - 1\\ - 1& 2 & -1\\ - 1&-1 & 2\end{pmatrix}\cdot v$ which...
  40. R

    Other Books about interpretation and philosophy of physics

    I'm studying physics with math as a minor and I'm currently at 4th semester. Don't get me wrong, I love studying physics. But I'm starting to feel that something is missing. Most of my courses are really focused on learning the formalism and technical methods, so we are able to solve different...
  41. B

    I New interpretation of quantum mechanics

    https://www.nature.com/articles/d41586-020-00120-6
  42. M

    MHB Geometric interpretation of maps

    Hey! :o We have the below maps: $f_1:\mathbb{R}^2\rightarrow \mathbb{R}^2, \ \ \begin{pmatrix}x \\ y\end{pmatrix}\mapsto \begin{pmatrix}-x \\ -y\end{pmatrix}$ $f_2:\mathbb{R}^3\rightarrow \mathbb{R}^3, \ \ \begin{pmatrix}x \\ y\\ z\end{pmatrix}\mapsto \begin{pmatrix}x \\ -y\\...
  43. Demystifier

    A The ontology problem of thermal interpretation

    I have already discussed the ontology problem of thermal interpretation (TI) of quantum mechanics (QM) several times in the main thread on TI. The following is supposed to be the final refined version of my argument, so I don't want it to be lost among other posts in the main TI thread...
  44. K

    I Questions on the Bohmian mechanics interpretation for instrumentalists

    Regarding the paper Bohmian mechanics for instrumentalists I like the ideas put forward in the paper because it provides a basis for an intuitive and logical explanation of quantum mechanics. I have many questions about it, but I will start with 3. Question 1: In this interpretation, what is...
  45. K

    I Thermal interpretation and EPR experiment

    [Moderator's note: Thread spun off from previous thread due to topic change.] The thermal interpretation of the double slit experiment is very appealing alternative explanation to the Bohmian interpretation as I understood it from these discussions...
  46. A

    I Interpretations of QM vs. statistical physics as an "interpretation"?

    Personally I tend to believe all (or almost all) of the interpretations of QM are unsatisfactory simply because they tell us something that we already know but do not tell us something we don't know. That is, they do not predict new phenomena or principles or properties of matter, etc. that can...
  47. Quantum Alchemy

    I Why can't there be a Universal Interpretation of Quantum Mechanics?

    Why can't there be a Universal Interpretation of Quantum Mechanics? If you unite Copenhagen and Many Worlds than all other interpretations will fall under the umbrella of a Universal Interpretation of Quantum Mechanics. The main problem with interpretations seems to be the role of the observer...
  48. binbagsss

    A Multi-particle state, wave-function with fewer zeros interpretation

    Hi , reading some notes on quantum hall effect, a comparison between Moore-Read wavefunction and Laughlin wavefunction is ' the moore-read state has fewer zeros suggesting the particles are more densely packed' Just confused with understanding why fewer zeros means the particles are more...
  49. T

    I Danger for the Many-Worlds Interpretation?

    Sabine Hossenfelder claims: This, of course, is not what we observe. We observe only one measurement outcome. The many worlds people explain this as follows. Of course you are not supposed to calculate the probability for each branch of the detector. Because when we say detector, we don’t mean...
  50. pinball1970

    I Sean Carroll podcast on many worlds interpretation

    Interpretation of quantum mechanics is something that is discussed at length on pf so it would be interesting to get views of the quantum guys on this short (30 mins) podcast. Thanks...
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